The idea is that if someone has only ever taken high-school math, they might think that mathematicians spend their time multiplying and dividing very large numbers; (“Are you even allowed to use calculators in your work?“). If someone has been lucky enough to take a first-year calculus course they might imagine that mathematicians solve harder and harder related rates questions. Going a step further, telling a mathematician that I study set theory often invokes brow-furrowing and questions like: “Don’t we already know everything about ordinals and cardinal arithmetic?“.

I was reading something the other day that argued that a lot of people become math majors because they’re good at applying procedures, since that’s mostly what they were exposed to in K-12. It’s kind of a shock for them when they find out that they’re expected to come up with new mathematical ideas and come up with new ways of proving things in mathematics…